Chapter 10: Using Graphs to Analyze Data

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Chapter 10Using Graphs to Analyze Data
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Vocabulary

• Mean
• Median
• Mode
• Outlier
• Range
• Frequency
• Histogram
• Line Plot
• Frequency Table

• Scatter plot
• Stem and Leaf Plot
• Box and Whisker Plot
• Central Angle

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Warm-up

• Write the numbers from least to greatest.
• 8, 6, 4, 9, 3, 5, 6
• 72, 68, 69, 71, 72
• 112, 101, 98, 120, 101
• 3.74, 3, 3.7, 3.3, 3.7

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Aim 10.0 Which measure of central tendency best
represents the data?

• Key Terms
• Mean, median and mode are measures of central
  tendency of a collection of data.
• Given the data 2, 3, 4, 5, 8, 8 and 12.
• The mean is found by
• The median is the middle number of the data.
• What is the median for the above data?
• How do you identify the median when you have an
  even amount of data?
• The mode is the number (s) that

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• Range is not a measure of central ___.
• To find the range you subtract the __ from the
  ___.
• Find the mean, median, mode and range for the
  following data. Round to the nearest tenth.
• 40, 45, 48, 50, 50, 59
• 2.3, 4.3, 3.2, 2.9, 2.7, 2.3

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• Outlier is a data value that is much greater or
  less than the other data values. An outlier can
  ____ the ____ of a group of data.

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Geography Use the map of Central America below.

• Which data value is an outlier?
• How does the outlier affect the mean?
• Hint Find the mean of all the numbers. Then find
  the mean again without the outlier. Last, find
  the difference of the means and explain how the
  outlier affects the mean.

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Find the outlier in each group of data below
and tell how it affects the mean.

• 9, 10, 12, 13, 8, 9, 31, 9
• 1,17.5,18, 19.5, 16, 17.5

• First, find the mean of the data.
• Then, find the mean again without the outlier.
• Compare the mean with the outlier and without.

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Choosing the best measure of central tendency

• Which measure of central tendency best describes
  each situation? Explain.
• a. The favorite movies of students in the eighth
  grade

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• Which measure of central tendency best describes
  each situation? Explain.
• a. The favorite movies of students in the eighth
  grade
• The mode, because the data is not numerical. When
  determining the most frequently chosen item, or
  when the data are not numerical, use the mode.

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• Which measure of central tendency best describes
  each situation? Explain.
• b. The daily high temperature during a week in
  July

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• Which measure of central tendency best describes
  each situation? Explain.
• b. The daily high temperature during a week in
  July
• Mean, since daily high temperatures in July are
  not likely to have an outlier. When the data have
  no outliers, use the mean.

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• Which measure of central tendency best describes
  each situation? Explain.
• c. The distances students in your class travel to
  school

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• Which measure of central tendency best describes
  each situation? Explain.
• c. The distances students in your class travel to
  school
• Median, since one student may live much farther
  from school than the majority of students, the
  median is the appropriate measure. When an
  outlier may influence the mean, choose the median.

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• Toshio found the following prices for sport
  shirts
• 20, 26, 27, 28, 21, 42, 18 and 20.
• Which measure of central tendency best represents
  the data? Explain.

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Summary Answer the following in complete
sentences.

• In a neighborhood with 46 homes, two are more
  than 6,000 sq.ft. in area.
• Would the mean or median provide a better
  measure of the typical home size?
• Explain your reasoning.
• Ten out of 20 students score a perfect 100 on a
  math test. Which of the following describes the
  score of 100 for the 20 students?
• mean, median, mode or outlier

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Warm-up

• Find the mean, median, mode and range of each
  data set.
• 1.Hours driving on a trip
• 6, 6.5, 7, 7, 8, 8, 9, 9.5, 10
• 2. Ages of cousins
• 8, 14, 13, 15, 12, 14, 17, 13
• 3. Low temperatures
• 4, -2, 0, -1, 2, -4, 5, 3

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Aim 10-1 How do we create a histogram and a
line plot?

• Key terms
• Frequency
• Frequency table
• Histogram
• Line plot

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Make a frequency table for the number of vowels
in the quotation below.

• The great glory of American democracy is the
  right to protest for right.
• Reverend Martin Luther King, Jr.(1929-1968)

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Frequency Table

• Display the data using a frequency table.
• 1, 4, 0, 3, 0, 1, 3, 2, 2, 4

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Making a Line Plot

• Make a line plot for these human body
  temperatures F.
• 98, 98, 99, 97, 98, 96, 99, 98, 97, 100, 99, 98,
  99

• What is the range for your data?
• Then create your line plot starting with the
  lowest number in your data and ending with the
  highest.

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Make a line plot for these human temperatures.

• 98, 98, 99, 97, 98, 96, 99, 98, 97, 100, 99, 98,
  99

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Displaying Data Using Intervals

• A survey measured the battery life of different
  brands of batteries used in portable stereos and
  CD players. Make a frequency table with intervals
  for the data below.
• Hours of battery life 12, 9, 10, 14, 10, 11, 10,
  18, 21, 10, 14, 22

• The data range is from 9-22. Your intervals must
  be equal-sized.

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• Hours of battery life 12, 9, 10, 14, 10, 11, 10,
  18, 21, 10, 14, 22

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Making a Histogram
Histogram is a special type of bar graph with no
spaces between the bars. The height of each bar
shows the frequency of data within the interval.
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Summary Answer in complete sentences.

• Why are frequency tables and line plots helpful?
• When is a frequency table with intervals or a
  histogram useful?
• How will the appearance of a histogram change if
  you use many small intervals instead of a few
  large intervals?

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Warm-up
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Warm-up

• The average price of a DVD player from 1997 to
  2002 is shown.
• Display the data in a line graph.
• How has the price of DVD players changed over
  time?

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Aim 10-2 How do we recognize and select an
appropriate scale?

• The same set of data may be graphed in different
  ways. Sometimes, however, a graph can give a
  misleading visual impression.

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Summary Answer in complete sentences.

• Explain what you would look for in a graph to
  see if the scale is an appropriate one.

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Aim 10-3 How do we create a stem-and leaf plot?

• A stem-and-leaf plot is a graph that shows
  numeric data arranged in order.
• Each data item is broken into a stem and a leaf.
• Ex Prices of portable MPS 3 players(dollars)
• 189, 214, 200, 195, 190, 192, 193, 211, 201, 196,
  195, 194, 205, 198, 208, 201

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Summary

• Explain how to read a stem-and-leaf plot.
• Explain how to identify the mode and median in a
  stem-and-leaf plot.
• Explain how we can use stem and leaf plots.

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Warm-up

• Write each percent as a decimal and a fraction
  in simplest term.
• 50 b. 33 1/3 c. 75 d. 20
• e. 10 f. 40 g. 37.5 h. 25

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Warm-up

• Find the median of each data set.
• 23, 32, 24, 22, 25, 24, 35
• 27, 15, 36, 27, 21, 28, 49
• 6, 2, 9, 3, 5, 4, 2, 9, 4,2, 3
• 90, 95, 92, 91, 95, 96, 97, 98, 96

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Warm-up

• Create a box and whisker plot with the following
  data. Then answer the questions below.
• 23, 32, 24, 22, 25, 24, 35
• 1. How many quartiles are there in a box and
  whisker plot?
• 2. What percent of the data falls below the 1st
  quartile?
• 3. What percent of the data falls above the third
  quartile?

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Aim 10-4 How do we create a box-and- whisker
plot?

• Box-and-whisker plot is a graph that summarizes a
  data set along a number line.
• Quartiles are the numbers that divide the data
  into 4 equal parts.
• Interquartile range (IQR) is the difference
  between the 1st and 3rd quartile.

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Identifying an Outlier

• To test if a number is an outlier it should be
  greater than 1.5 times the IQR.

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Creating a box-and-whisker plot

• 10, 16, 24, 11, 35, 26, 29, 31, 4, 53, 47, 12,
  21, 24, 25, 26

• Step 1 Arrange the data from least to greatest.
• Step 2 Find the median.
• Step 3Find the lower and upper quartile.

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Number Sense

• By looking at a box-and-whisker plot can you
  determine if there is an outlier?
• The mean?
• The mode?
• The range?
• Explain.
• Where do you think a box-and-whisker plot are
  used?

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Summary

• Explain how to create a box-and-whisker plot.

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Ticket out

• On the post-it note write your complete heading.
• Make a box-and-whisker plot for the data below.
• 10,13, 16, 17, 20, 22, 23, 24, 26, 30, 31

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Warm-up

• Make a box-and-whisker plot for data below.
• 9, 8,1, 8, 7, 6, 3, 7, 9, 8, 6, 4,7, 8, 9, 10,
  10
• What percent of the data is above the first
  quartile? Third quartile? Between the 1st and
  lower and upper quartile?

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• Given the above box and whisker plot,
• What is the 1st quartile and 3rd quartile?
• What is the interquartile range?
• Now find 1.5 x the interquartile range.

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Aim 105 How do we create a scatter plot?

• Scatter plot is a graph that displays two sets of
  data as an ordered pair. It can help you decide
  whether one set of ___ is related to ____.

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Using Scatter Plots to Find Trends

• Positive correlation or Positive trend
• Negative correlation or Negative trend
• No correlation or no trend
• A trend line is a line you draw on a graph to
  approximate the relationship between the sets of
  data.

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Summary

• Do you think predictions made from a trend line
  will always be accurate? Explain why or why not?

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Warm-up

• Would you expect a positive, negative or no
  correlation between each pair of data sets?
  Explain.
• The age of pets in a home and the number of
  pets in that home
• The temperature outside and the number of layers
  of clothing
• Your grade on a test and the amount of time you
  studied
• The shoe sizes and the shirt sizes for men

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Warm-up

• Solve the proportion.
• 2 16 x 5 7 r
• 3 y 12 2 3
  12
• 25 75
• p 125

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Aim10-6 How do we read and create a circle
graph?

• A circle graph is a graph of data where the
  entire circle represents a whole.
• Each part of the graph represents a part of the
  whole.

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Making Circle Graphs

• To make a circle graph you must find the measure
  of the central angle. The central angle is an
  angle whose vertex is the center of the circle.

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Example Environment

• Endangered species
• Group of species
• Mammals 342
• Birds 273
• Fish 126
• Reptiles 115
• Clams 72
• Insects 48
• Other 94

• First add the of species.
• Then use a proportion to find the measure of the
  central angles.
• 342 x
• 1070 360?? ?

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• After you find the measure for each angle, you
  can create your circle graph.
• Draw your circle using a compass or protractor.
  Make the center of the circle and draw a radius.
  Construct a central angle with a protractor.

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• Construct the other central angles using a
  protractor.
• Label each sector and title you graph.

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Practice Make a circle graph for the set of data.

• Fuel Used by Types of Vehicles
• (billions of gallons)

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Summary

• Explain how a circle graph represents data.
• How do you create a circle graph?

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Warm-up 8-18-09

• Make a frequency table and histogram for the data
  set below. Use intervals of equal size to group
  the data.
• Miles walked at a walk-a-thon
• 1, 6,9, 10,12,15, 16, 18, 19, 20, 10, 8, 5, 2, 6,
  9, 5, 13, 14, 18, 10, 9, 11, 14, 15

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Review

• Create a box and whisker plot.
• 93, 75, 87, 83, 99, 75, 80, 72,
• 77, 95, 98, 82, 87, 100, 91, 68
• Then find the interquartile range.
• Fill-in the blanks below.
• The outlier is a number that lies greater than__
  and less than___.

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Aim 10-7 How do we choose an appropriate graph?

• The type of graph you choose is based on your
  data.
• Scatter plot if you are looking for a trend or a
  relationship.

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• Bar graph when the data falls into distinct
  categories and you want to compare totals.

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• Line graph when the data shows a gradual increase
  or decrease over time.

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• Circle graph when you want to show how each part
  makes the whole.

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Summary

• What factors go into your decision about what
  kind of graph is appropriate for a given set of
  data?

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Warm-up 8-19-09

• Given the following data. Find the mean, median,
  mode and range.
• 95, 94, 91, 94, 93, 93, 91

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Aim 12-8 How do we choose a sample for a survey
of a population?

• How many books you read each week? What are your
  hobbies?
• Statisticians use questions like these in surveys
  to get information about specific groups.
• A population is a group about which you want
  information. A sample is a part of the population
  you use to make estimates about the population.
  The larger your sample, the more reliable your
  estimates will be.

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• For a random sample each member of the population
  has an equal chance to be selected. A random
  sample is likely to be representative of the
  whole population.

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Real-World Problem Solving

• You want to find out whether students will
  participate if you start a recycling program at
  your school. Tell whether each survey plan
  describes a good sample.
• Interview every tenth teenager you see at a mall.
• This sample will probably include students who
  do not go to your school. It is not a good sample
  because it is not taken from your population you
  want to study.

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Real-World Problem Solving

• You want to find out whether students will
  participate if you start a recycling program at
  your school. Tell whether each survey plan
  describes a good sample.
• Interview the students in your ecology class.
• The views of students in an ecology class may
  not represent the views about recycling of
  students in other classes. This is not a good
  sample because it is not random.

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Real-World Problem Solving

• You want to find out whether students will
  participate if you start a recycling program at
  your school. Tell whether each survey plan
  describes a good sample.
• Interview every tenth student leaving a school
  assembly.
• This is a good sample. It is selected at random
  from the population you want to study.

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Answer in complete sentences.

• Explain whether each plan describes a good
  sample.
• You want to know which bicycle is most popular.
  You plan to survey entrants in a bicycle race.
• You want to know how often teens rent videos. You
  want to survey teens going into the local video
  store.
• You want to know the most popular breakfast
  cereal. You want to survey people entering a
  grocery store.

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Making Estimates About Population

• You can use a sample to make an estimate about a
  population by writing and solving a proportion.
• Example
• From 20,000 calculators produced, a manufacturer
  takes a random sample of 500 calculators. The
  sample has 3 defective calculators. Estimate the
  total number of defective calculators.

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Solution
About 120 calculators are defective.
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Check for Understanding

• Using Sample B, how many of 20, 000 calculators
  would you estimate to be defective?
• Would you expect an estimate based on Sample C to
  be more accurate or less accurate than one based
  on Sample B? Explain.
• Explain why you would take a sample rather than
  counting or surveying an entire population.

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Summary Answer in complete sentences.

• Eight of the 32 students in your math class have
  a cold. The school population is 450. A student
  estimates that 112 students in the school have a
  cold.
• Why is your math class not a representative of
  the population?
• Describe a survey plan you could use to better
  estimate the number of students who have a cold.

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Aim 10-8 How do we solve a problem by combining
strategies?

• Strategies
• Draw a diagram
• Look for a pattern
• Make a Graph
• Make an Organized List
• Make a Table
• Simulate a Problem
• Solve a Simpler Problem

• Try, check and revise
• Use Logical Reasoning
• Work Backwards
• Write an Equation

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Summary

• How does drawing a diagram or using logical
  reasoning help you solve a problem?